Confinement of positive ions with a static electric and magnetic field

11.
Confinement of positive ions and electrons with a static electric and magnetic field

Just some idea's...11e idea

The goal is to design a kind of
fusor (Wikipedia.org/wiki/Fusor ). But instead of a fixed inner grid, which causes
losses, we try to confine positive H+ and B+ ions with a static
electric field and a static magnetic field.

We'll use our computer simulation program,
as described in: 10b computer simulation(by the way:
also other type of ions can be used,
for example deuterium
ions)

Above
and under the sphere (or around) a magnet is placed which generates a vertical magnetic field inside the sphere.
We'll try out several magnetic field configurations in the computer program.

An electric field is created by placing
eight point charges: four near the top and four near the bottom. In a real apparatus this
could be done different (perhaps with rings? see
applet), but in order to simulate it easily in
our computer
program we'll do it at the moment in this way (with point charges). In the
middle of each side is also a point charge placed.

Fig. 2.
The simulation space, with four positive point charges above and four under
( and one in each side; not in the drawing).

The movement of the positive ions is simulated using
Leap-frog integration (see
10.1 experiment10 ).
The ions interact amongst themselves and with the electric and
magnetic field applying the Coulomb and Biot-Savart formulism (
non-relativistic).

Conclusions so far.

If we use a constant
magnetic field of about 1 or 2 T (should be possible to realize..),
and a constant electric field generated by the point charges as
described before, the positive ions are confined in the simulation
space. Even if we give them an initial speed up to 0,5E6 m/s in all
directions. At least they are confined during the (very) short time
of simulation.

The magnetic field is important: if it is decreased the ions
escape away to the sides.

No interactions (collisions) between the ions are observed. The
reason of this is, probably, because the ions are relatively very
small and there are only a very few (in reality there would be
millions..). When the charge of the ions is increased a 10000000 times,
then yes interactions between them are observed. I let one H+ and
one B+ ion collide with each other. If the charge is increased
100000 times and dt= 1.59E-14, then they did not collide With
dt=1.59E-15 and 100000 times more charge they do collide. (dt
= Δt = the
integration time, see
10.1 experiment10)

So far so good.... Could this be a fusor without inner
grid? I did a search in internet, but could not find
anything similar.. It should be almost impossible that this simple
idea has not been tried out already..... However, I got this idea
because I have my program, with which I can try out easily different
kind of configurations. It took me quite a long time to develop it;
could it be that I am the only one so far with a simulation program like
this?

Perhaps there is some error in the software, perhaps it
works only with a few ions (and not with millions) and with non relativistic formulas;
perhaps it works only for the very short simulation time
(about 3E-5 s) ; perhaps the ions stay
confined but will not fuse.... (in a fusor with inner
grid they move towards the centre; here they move "more or less"
towards the centre). Perhaps the accelerating and
decelerating of the ions causes to many losses..
(bremstrahlung).
But until I have proof that it cannot produce net energy, I should
continue, because there could be a small change that it does
work.... Anyway it's fun to work on it
☺

To check the correctness of the simulation, we will
calculate the total energy of all particles.

The kinetic energy of all moving particles is calculated (electrons, H+ and
B+ ions).
The potential energy between H+-H+, H+-B+, H+-point charges,
B+-B+, etc. is calculated.
When the potential energy between equal particles is calculated in two
loops, in the end we divide by 2, see also
10.9 experiment9
.
Note: also the potential energy of the moving particles with respect to the
fixed charges is calculated. The potential energy of the fixed charges
amongst themselves is
not calculated (is constant).

Part of the program:

for i:=1 to (AmountB) do
begin //*
xi:=boron[i].x;
yi:=boron[i].y;
zi:=boron[i].z;

f or j:=1 to AmountH do
begin
xj:=hydrogen[j].x;
yj:=hydrogen[j].y;
zj:=hydrogen[j].z; {K is Coulomb's constant, see unitB}
r:=sqrt( sqr(xi-xj)+sqr(yi-yj)+ sqr(zi-zj) );
if boron[i].exists and hydrogen[j].exists then Ue:= Ue+ K*qe*qe/r;
{neither we have to divide by 2, because we do not calculate double
pairs like we did with the electrons}
end;
end; //*

The positive charge of each fixed point charge is:
5.56E-7 Q (100 kV for a sphere with diameter 10 cm), the magnetic field
constant 1 tesla, generated 200 H+ and 200 B+ with initial random speed < 0,5E6 m/s. With dt=1E-9 s no ions escaped and the total energy
of the particles stayed constant.

Conclusion:

The total energy of the moving particles stayed constant (within
limits) and they
stayed confined in the simulation space. Good! ☺

When positive charged ions collide, some of them can get higher speeds
and could escape. This could perhaps be prevented by two charged grids, as
shown in figure 3:

Fig. 3. Schematic
representation of an electrostatic magnetic fusion device with two grids
near the outer wall

The negatively charged grid must be close enough, so it does not produce
a "negative" electric field inside the sphere. But also it must be open
enough (with holes), to prevent that too much positive ions collide with it,
producing unwanted losses.

Our simulation space is a cube with a side of 1 m.
Let's take the magnetic field strength 1 tesla.
What is the maximum horizontal speed of the ions so that r <= 0,5 m? (non
relativistic)

Also in
hyperphysics it is suggested that the
currently attainable particle energies in thermonuclear reactors is in the
range 1-10keV, corresponding to
0.77E7 K- 0.77E8 K. Filling in
0.77E8 K inhyperphysicswe get v
≈
1E6 m/s (for a deuterium ion).

This temperature-speed calculations are not very correct/detailed, but anyway we get
some idea
about it.

It seems to be that with a magnetic field of 1 tesla we could more or less
confine D+ particles up to about 2,4E7 m/s. This is ten times higher
than the speed needed to fuse ... So the confinement
to the sides seems to be okay.

In the simulation program we gave the ions
an initial random speed in all directions of 0.5 E6 m/s . This is 25 % of the
speed needed for D+ to fuse.
If we increase this initial speed, some particles escape upwards and
downwards (with B=1 T and 200 kV).

Conclusion:

The problem is to confine the fasted
particles upwards and downwards. Increasing the B-field and/or
potential is not very attractive.. Perhaps we could place more point
charges up and down.

We will investigate this
further..

We increased the electric field by creating more positive point
charges above and increasing the voltage to 300 kV; applied a magnetic field
of 1,5 tesla; generated 20 H+ and 20 B+ ions with an initial speed up to 1,5E6
m/s in all directions, and the ions stayed ... confined!

Instead of hydrogen and boron, we will use now only deuterium ions. Massa
D+ = 2 x massa H+ . B=1 tesla and 200 kV, initial speed up to 1,5E6 m/s.
The ions stayed confined. Also with B=0,7 tesla and 90 kV they stayed
confined.

According to experiment
11.7 it seems to be possible to confine positive H+ and B+ ions with
random speeds in all directions up to 1,5E6 m/s, in a reasonable
(realizable) constant magnetic field of 1,5 tesla and in a
reasonable constant electric field . (I assume the
electric field is realizable... ).

In experiment 11.8 we used
only D+ ions (30 particles, also
with random speeds in all directions up to 1,5E6 m/s).
With B=1 tesla and 200 kV (potential of the point
charges if it would be little spheres with radius 5 cm). The
ions stayed good confined.

In experiment 11.9 we used
D+ ions (30 particles, random
speeds in all directions up to 1,5E6 m/s).
With B=0,7 tesla and 100 kV (potential of the point
charges if it would be little spheres with radius 5 cm). The ions stayed also
good confined.

For fusion to occur, it seems to be necessary to have an amount of
10^18 ions per
cubic meter= 1E18 . 1,6E-19 C = 1,6 C ( a lot of charge).
If it is mixed with electrons, the net charge will be less. But what do
these electrons?

In the program we use positive point charges. In
reality these will be conductors. The positive charge will move
to the outside and this will decrease the E-field in the inside of
the vacuum chamber...? See the screenshot of an applet in fig.
8b. This is not good ...

I shall have to simulate positive charged conductors, place them
in the vacuum chamber and see what happens.

Or would it be possible to charge a non-conducting object, which
then can be considered as a point charge?

If we use for the up and down positive charges a ring, the
electrons are attracted to the ring, but fly through it and will move
up and down.. I see this happening in the simulation if I generate
electrons. Perhaps an idea.

If I charge the point charges in the middle of the vertical side negative,
the ions keep trapped. This is quite similar to the already existing
Penning trap:
Wikipedia./Penning_trap . I did not know about this, just invented it
more or less again. They got the Nobel Price for it.....

The problem of this Penning trap is that it can confine only ions of one
type (or positive, or negative), and only a few.

Would it be possible to modify it to trap both electrons and positive
deuterium ions?

We will put some negative point charges in the centre of the top and the
bottom side.

The vacuum chamber is pumped empty. Only some deuterium
gas is discharged inside. (The best way to do this should be investigated:
perhaps most favourable is to inject it along the vertical centre line.) This gas is ionized
(I suppose) into D+ ions and electrons
because of the electric field .

The electrons (more or less near the vertical centre
line) are attracted by the two positively charged rings and move upwards and
downwards in a spiral-shaped path. The vertical magnetic field of 1 tesla
prevents them to escape sideward. Once they move through the ring they will
be repelled by the negatively charged ellipsoid and move back towards the
centre. In this way the electrons will oscillate between the blue ellipsoids
and the centre of the vacuum chamber. (this is what happens in the
simulation)

The D+ ions (more or less near the vertical centre
line) are repelled by the two positively charged rings and will vertically
oscillate around the centre of the vacuum chamber, also in a spiral-shaped
path. (this is what happens in the simulation)

In a "traditional" fusor the positive ions move towards the centre (a
point). However, only when they are outside the inner grid they feel the
force towards the centre. Once they are inside the inner grid (and they have
not collided with it), they will not feel this force any longer (if I am not
wrong).

In our S.E.M. fusor the D+ will oscillate in a vertical movement (al
least in the simulation..). Will the same happen as in a traditional fusor:
the positive D+ ions are confined and attracted towards the centre;
they collide between each other; some of them get as a result of these
collisions higher speeds; some ions with higher speeds collide between each
other and fuse..... ?

In the simulation there are only a few particles (it
is not possible to have more than a couple of hundreds, otherwise it's takes
too much memory of the computer and the simulation speed becomes too small).

In the program it is possible to turn on and off the interaction between
the particles. When there are only a few particles, it hardly
influences the speed of the simulation, but when there are more particles,
more then 100, then the simulation is running faster with the interaction
turned of.

In the real world possibly a cloud of electrons and deuterium ions (mixed
together: a plasma), will be confined more or less in the centre of
the vacuum chamber.

Maybe we should construct this new type of fusor. It seems to be not
too difficult (at least not a lot more difficult than a traditional fusor),
and see what happens..

At the moment I will continue with the simulation program: visualize the
electric field, simulate charged ring and ellipsoid conductors , do more
experiments..

With an initial random speed < 3E6 m/s (!) the D+ and the e- kept confined
in the simulation space (during the short simulation time).

Although the simulation had been running about 48 hrs, the real
simulation time is very small: 1,2E-5 s.
What I fear is that the particles will spread out sidewards after a larger
time period.
I will program the maximum distance r from the vertical centre of the
particles and see if it increases.
It did not seem to increase during some experiments I did.

The electrons are now more confined in the centre, but
the D+ ions spread more out in the vertical direction, although they
do not escape (during the short simulation time). The D+ ions seem to obtain
more speed in this configuration (= higher temperature). This would be an
advantage to obtain fusion.. Furthermore, the electrons perhaps form a
kind of virtual cathode that will attract the D+ ions towards the centre.

Fig. 7b.

In the experiment of figure 7b. the positive middle
ring has been deleted. The electrons still stay confined and the D+ ions
will obtain an higher speed in the centre (I suppose) compared with the
configuration of figure 7a. Higher speed (is higher temperature) means more
change of nuclear fusion.. However the confinement of the electrons is less
compared with the configuration with a middle ring.

The simulation program got stuck (did not proceed any longer) with this
amount of particles.
What can be seen is that the electrons seems to concentrate near the centre.
Perhaps in a real device they would form a kind of virtual cathode and
attract the positive deuterium ions towards the centre.

Maybe we could use a small inner grid ( as in a Farnsworth fusor) to
start the operation .

Fig. 12. SEM fusor with small inner starting grid

What polarity is the best to be used we should investigate. (fig. 6 or
fig. 7). We could construct an experimental SEM fusor with the possibility
to reverse the polarities and try out.

Possible modus operandi:
Pump vacuum.
Let in a little bit deuterium gas. (Or inject deuterium ions? But then no
inner starting grid will be necessary.)
Switch on the electromagnet.
Put on the voltages of the rings, small spheres and the inner grid.
The inner grid will burn, but an amount of D+ ions will have concentrated in
the centre.
Inject electrons? To form a virtual cathode? (for example as in fig. 9
or fig. 7)

The electrons represent the greatest loss and maximal heating component
of the traditional fusor. They are accelerated just like the deuterium ions, but
towards the shell wall. They slam into it producing x-rays and accounting
for the bulk of the heating of the outer shell wall. See:Fusor.net detailed theory of operation

In
www.researchgate.net/is mentioned "generally, for
distances of about 1 cm and pressures of about 10^-7 torr the dielectric
strength is ranging from 200 kV/cm to 400 kV/cm. Even larger values are
possible for lower pressures".

In Wikipedia.org
"Field emission in pure metals occurs in high electric fields: the gradients
are typically higher than 1 gigavolt per metre".

So it seems to be that we will not have problems with dielectric breakdown
or field emission, if our fusor has a good vacuum.

---

Applying a mirror magnetic field to the SEM fusor and see if this
will improve it.

By doing so we can decrease (a little bit) the voltages of the charged
rings and spheres.

---

It is not possible to simulate more than a couple of hundred particles,
because lack of computer power.
But let's see what happens if we both increase the mass and the charge of
the ions and electrons.
See: Droom11.15.htm

----

In
alpha.web.cern.ch/penningtrapa device a little bit simular to the SEM fusor
is used, but not for fusion. Here the goal is to trap antiprotons and
positrons in order to produce antihydrogen. According to them the electrons
cool down due to cyclotron_radiation .
"Antiprotons,
however, are far more massive. It would take antiprotons over 300 years of
sitting in a 1 Tesla magnetic field to cool through cyclotron radiation
alone!"
That the electrons cool down in the SEM fusor is only favorable, I think. So
they form even better a negative cloud: a virtual cathode (I suppose). The protons
however should be hot, move with high speeds in order to be able to fuse.

"At the center of the Sun, fusion power is estimated by
models to be about 276.5 watts/m3. Despite
its intense temperature, the peak power generating density of the core
overall is similar to an active compost heap,
and is lower than the power density produced by the metabolism of an adult
human."